Find all solutions for the given triangle, if possible. If no solution exists, write no solution. Round side lengths to the nearest tenth and angle measures to the nearest degree. $a=5, b=6, A=63^{\circ}$

Are each of the following lengths of chords in the circle? Write yes or no for each statement.

A. AC=13.5

B. EF=7.1

C. BF=2.9

Explain why the following form linearly dependent sets of vectors. (Solve this problem by inspection.)

$u_1=(3,-1), u_2=(4,5), u_3=(-4,7)$ in $R^2$

A 10.0 kg block with a charge of $+8.00 \times 10^{-5} \mathrm{C}$ is placed in an electric field $\vec{E}=(3000 \hat{\mathrm{i}}-600 \hat{\mathrm{j}}) \mathrm{N} / \mathrm{C}$. What are the magnitude of the electrostatic force on the block?

For the right triangular prism found in previous Exercise, suppose that the sides of the triangular base measure $3 \mathrm{ft}, 4 \mathrm{ft}$, and $5 \mathrm{ft}$. The altitude is $6 \mathrm{ft}$ in length.

a) Find the lateral area of the prism.

b) Find the total area of the prism.

c) Find the volume of the prism.

Use the tangent to find the unknown side length.

Find QR.

The length of the sides of the triangle are $\overline{AB}=81.5$, $\overline{BC}=32$, and $\overline{AC}=75$.

Find the volume of the right prism or right cylinder. Round your answer to two decimal places.

The prism has length of 9 inches, width of 7 inches and height of 3 inches.

MPS, Inc, has the following unadjusted account balances as of December 31, 2015, the company's year-end:

• Cash: $430,000
• Accounts Receivable:$2,000
• Prepaid Insurance: $14,000
• Prepaid Rent:$22,000
• Equipment: $60,000
• Accumulated Depreciation-Equipment:$0
• Accounts Payable: $10,000
• Common Stock:$16,000
• Sales Revenue: $823,100
• Wage Expense:$290,400
• Utilities Expense: $11,200
• Insurance Expense:$8,500
• Rent Expense: $11,000
• Depreciation Expense-Equipment: o

At year-end, MPS makes adjusting journal entries to properly record revenues and expenses. The following information applies to the adjusting journal entries:

• The prepaid insurance balance relates to an insurance policy purchased on January 1, 2015, that covers the period of 1 / 1 / 15-12 / 31 / 15.
• The prepaid rent balance relates to rent paid in June 2015 to cover the period of 7/1/15-6/30/16.
• Wages for 2015 in the amount of$26,000 will be paid after year-end and have not yet been recorded.
• MPS purchased the equipment in the beginning of January 2015 and will depreciate it on a yearly basis. No depreciation has been recorded yet. The equipment has a useful life of 15 years, no residual value, and will be depreciated on a straight-line basis. Prepare the journal entries necessary to record the adjustments at year-end.

MPS, Inc, has the following unadjusted account balances as of December 31, 2015, the company's year-end:

• Cash: $430,000
• Accounts Receivable:$2,000
• Prepaid Insurance: $14,000
• Prepaid Rent:$22,000
• Equipment: $60,000
• Accumulated Depreciation-Equipment:$0
• Accounts Payable: $10,000
• Common Stock:$16,000
• Sales Revenue: $823,100
• Wage Expense:$290,400
• Utilities Expense: $11,200
• Insurance Expense:$8,500
• Rent Expense: $11,000
• Depreciation Expense-Equipment: o

At year-end, MPS makes adjusting journal entries to properly record revenues and expenses. The following information applies to the adjusting journal entries:

• The prepaid insurance balance relates to an insurance policy purchased on January 1, 2015, that covers the period of 1 / 1 / 15-12 / 31 / 15.
• The prepaid rent balance relates to rent paid in June 2015 to cover the period of 7/1/15-6/30/16.
• Wages for 2015 in the amount of$26,000 will be paid after year-end and have not yet been recorded.
• MPS purchased the equipment in the beginning of January 2015 and will depreciate it on a yearly basis. No depreciation has been recorded yet. The equipment has a useful life of 15 years, no residual value, and will be depreciated on a straight-line basis. Prepare the journal entries necessary to record the adjustments at year-end.

a. Prepare an unadjusted trial balance for MPS, Inc. as of December 31, 2015.

Carlos is the last person to board a Ferris wheel that has a radius of 52 feet. The counterclockwise arc swept out by Carlos is measured from where he got on, at the bottom of the Ferris wheel. Since Carlos is the last one to board, the Ferris wheel starts up and doesn't stop again unit the ride is over. a. Draw a diagram that show's Carlos's location and the angle swept out by Carlos at an arbitrary moment in time. b. Define a function f that relates Carlos's vertical distance above the center of the Ferris wheel (measured in feet) as a function of the measure of the angle (in radians) swept out by Carlos. Over what interval of input will Carlos complete one revolution? c. Define a function g that relates Carlos's horizontal distance to the right of the center of the Ferris wheel (measured in feet) as a function of the measure of the angle (in radians) swept out by Carlos Over what interval of input will Carlos complete one revolution? d. Suppose Carlos's cart is traveling 0.3 radii per second on a circular path as the wheel rotates. Define a function h that relates Carlos's horizontal distance to the right of the center of the Ferris wheel (measured in feet) as a function of the time since beginning the ride (measured in seconds). How long will it take for Carlos to complete one revolution? e. Marilyn claimed that she saw Carlos's cart travel at a speed of 3.5 radii per second. Is that possible? Explain. (Hint: Determine the cart's speed in miles per hour. f. Suppose that Carlos's cart traveled at 0.4 radii per second. Define a function j that relates Carlos's horizontal distance to the right of the center of the Ferris wheel (measured in feet) as a function of the time since beginning the ride (measured in seconds). How long will it take for Carlos to complete one revolution? g. Suppose Carlos's cart is traveling 0.2 radii per second. Define a function k that relates Carlos's horizontal distance to the right of the center of the Ferris wheel (measured in feet) as a function of the time since beginning the ride (measured in seconds). How long will it take for Carlos to complete one revolution? h. Sketch a graph of each function defined in parts (d)-(g). Label your axes. Identify the interval of input over which Carlos completes one revolution.

The person in this diagram is making an observation to find his angular distance along Earth's surface from (1) the equator (2) the Prime Meridian (3) Polaris (4) the North Star

A newspaper rated several restaurants by cost, level of service, atmosphere, and location using a scale of $\star$ being low and $\star \star \star \star$ being high.

$$\begin{aligned} &\text { Restaurant Cost Service Atmosphere Location }\\ &\begin{array}{c|c|c|c|c} \hline \text { Catalina Grill } & \star \star & \star & \star & \star \\ \hline \text { Oyster Club } & \star \star \star & \star \star & \star & \star \star \\ \hline \text { Casa di Pasta } & \star \star \star \star & \star \star \star & \star \star \star & \star \star \star \\ \hline \begin{array}{c} \text { Mason's } \\ \text { Steakhouse } \end{array} & \star \star & \star \star \star \star & \star \star \star \star & \star \star \star \\ \hline \end{array} \end{aligned}$$

Write a $4 \times 4$ matrix to organize this information.

In this exercise, find the mass of the following solid with the given density function. Note that density is described by the function f to avoid confusion with the radial spherical coordinate $\rho$.

The solid cylinder $\{(r, \theta, z): 0 \leq r \leq 2,0 \leq \theta \leq 2 \pi$, $-1 \leq z \leq 1\}$ with a density $f(r, \theta, z)=(2-|z|)(4-r)$

You observe light coming from a distant star and determine that most of the visible light coming from the star is in the blue part of the visible light spectrum. Which of the following pieces of information do you now know about the temperature of the star?